Page 21 - DMTH404_STATISTICS

Sachin Kaushal, Lovely Professional University Unit 2: Methods of Enumeration of Probability

Unit 2: Methods of Enumeration of Probability Notes

CONTENTS

Objectives
Introduction
2.1 Probability : Axiomatic Approach
2.1.1 Probability of an Event : Definition

2.1.2 ProbabJlity of an Event : Properties
2.2 Classical Definition of Probability
2.3 Summary
2.4 Keywords

2.5 Self Assessment
2.6 Review Questions
2.7 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss probabilities to the outcomes of a random experiment with discrete sample space,
 Explain properties of probabilities of events, I

 Describe the probability of an event,
 Explain conditional probabilities and establish Bayes theorem,

Introduction

In this unit, we shall introduce you to some simple properties of the probability of an event
associated with a discrete sample space. Our definitions require you to first specify the probabilities
to be attached to each individual outcome of the random experiment.
Therefore, we need to answer the question : How does one assign probabilities to each and
every individual outcome? This question was answered very simply by the classical probabilists
(like Jacob Bernoulli). They assumed that all outcomes are equally likely.

Therefore, for them, when a random experiment has a finite number N of outcomes, the
probability of each outcome would be 1/N. Based on this assumption they developed a
probability theory, which we shall briefly describe in Sec. 6.4. However, this approach has a
number of logical difficulties. One of them is to find a reasonable way of specifying “equally
likely outcomes.”
However, one possible way out of this difficulty is to relate the probability of an event to the
relative frequency with which it occurs. To illustrate this point, we consider the experiment of
tossing a coin a large number of times and noting the number of times “Head” appears.

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